Differential spectral topographic analysis (DISTA)

ABSTRACT

The present invention provides a new analysis based on Differential Spectral Topographic Analysis (DISTA). Using data from the spectral methods known in the art, DISTA is based upon the normalization of the spectra to a fixed topographic space, creating a set of spectral forms, and the summation of the absolute differences in topography between one or more reference spectra and the test spectra taken at different magnitudes of the perturbing parameter. This method allows for a sensitive estimate of the fraction of form A and form B of an entity of interest. This method also allows for the calculation of apparent free energy from the conversion of the entity of interest from a first to a second form where appropriate, and in the alternative, calculation of a fraction of structural changes.

GOVERNMENT INTEREST

The invention described herein may be manufactured, licensed, and usedfor United States governmental purposes without the payment of anyroyalties to the inventors or assignee.

BACKGROUND OF INVENTION

1. Field of Invention

This invention relates to a new method of spectroscopic analysis todetermine the fraction of conversion of a physical configuration of asystem of interest from a first configuration to a second configuration,and in particular, a method to determine respective fractions of twodifferent forms of a molecule in solution. It has broad applicability tothe fields of medicine, agriculture, and biotechnology.

2. Description of the Related Art

The field of spectroscopic analysis seeks, among other characteristics,the configuration of molecules of interest. A molecule often studied isthe protein and a configuration of interest is its three dimensionalstructure. As those in the art recognize, a protein exhibits a specificthree-dimensional structure which is critical to activity and function.That three-dimensional structure (also known as the native or foldedstate) is sensitive to a variety of factors, such as pH, temperature,pressure, or the presence of a denaturant such as urea.

Spectroscopic analysis of proteins is made possible by a protein'sability to absorb light over a wide spectrum and to re-emit it in acharacteristic fashion as well as the change in absorbance and emissiondue to a perturbation of the structure. The three most popular modes ofspectroscopic analysis today are based on the absorbance/emission ofvisible light (the absorbance spectrum), differential absorbance ofpolarized light (circular dichroism), and fluorescent light. All threemodes are sensitive to the three-dimensional structure of a protein. Forexample, fluorescence emission intensity can be used to gauge the changeof molecular configuration as function of some parameter expected toeffect the stability of the test molecule. As noted above, thisparameter might be pH, some denaturant such as urea, or an extensiveproperty of the system such as temperature or pressure. Practitionershave also used the ellipticity signal at 222 nanometers from circulardichroism (θ₂₂₂, CD) to estimate the extent of unfolding in proteinshaving a significant α-helical content.

Nonetheless, each of these methods suffers in adequately testing theproportions of folded state. Fluorescence intensity analysis is highlytemperature sensitive. Fluorescence analysis depends on the assumptionthat the magnitude of a spectroscopic signal at one wavelength willremain a constant function of whether the molecule is in its folded orunfolded form. Thus, the analysis requires that two constant signalsexist, one for each form, and that each constant signal be independentof the variation of the perturbing parameter. If this does not occur, asis the case when temperature is the perturbing factor, a correction mustbe applied. One correction commonly applied is based on Taylor seriesexpansions of unknown functions multiplied by an exponentially decliningtemperature term, E. A. Permyakov, The Luminescent Spectroscopy ofProteins (CRC Press 1993) at pp. 99-107. Although some in the art assertthat protein structure as a result of heat denaturation can be studiedon a quantitative basis using data so corrected, such data frequentlyyields coefficients which predict infinite emission intensities in thetemperature range from 0° C. to 100° C. Thus the method is often not asreliable as desired over the important temperature range which includesboth cold and heat denaturation.

Another important method for determining the denaturation of the proteinstructure, or extent of exposure of fluorophores to the environmentexternal to the protein, is fluorescence quenching, Joseph Lakowicz,Principles of Fluorescence Spectroscopy (Plenum Press 1983) at pp.279-284. In this method the protein is exposed to varying levels of aquencher such as iodide which cannot interact with fluorophores buriedin the protein interior. The percentage of exposed fluorophores can thenbe calculated using the Stern-Volmer equation:${\frac{F_{0}}{\Delta \quad F} = {\left( {\frac{1}{f_{a}}*\frac{1}{K_{sv}}*\frac{1}{\lbrack Q\rbrack}} \right) = \frac{1}{f_{a}}}},$

where F₀ is initial fluorescence intensity at the test wavelength atzero concentration of quencher Q, ΔF is the initial fluorescenceintensity minus the fluorescence intensity at a given concentration ofquencher, f_(a) is the fraction of initial fluorescence accessible tothe quencher, K_(SV) is the Stern-Volmer constant, and [Q] is theconcentration of quencher Q. However, this cannot easily be related tothe percent of protein unfolded because it provides no information aboutthe spectral characteristics of the unquenched fluorophores. Thus, if aprotein has two domains, which can be referred to as A and B, with thesame number of buried fluorophores, then A may heat denature at a lowertemperature than B, but B may cold denature at a higher temperature thanA. In this case the Stern-Volmer analysis will show that the proteinappears to be increasing the percentage of exposed fluorophores at lowtemperature and the percent increased exposure could be scaled, usinginterpolation or normalization techniques, between the initial value andthe heat denatured value to estimate a percent of unfolded protein. But,in fact, a different part of the protein would be unfolding.

In the case of θ₂₂₂ measurements of proteins, one must assume that theshift at that wavelength or the change in signal accurately reflects thehelical content of the protein, that the change in helical contentreflects accurately the fraction of unfolded protein, and that theprotein domain which is unfolding is where the helices are.

It has been generally accepted for quite some time that the helicalsignal depends strongly on the length of the helices even when totalhelical content is constant, Y. H. Chen, et al., Biochemistry 13:3350(1974). Also, helices are often quite stable at low temperature as shownby J. M. Scholtz et al., Proc. Natl. Acad. Sci., USA 88:2854 (1991).Thus low temperature tertiary unfolding may leave helical secondarystructures intact and the helices may appear longer, i.e., have largermagnitude CD signals, such that the secondary structure may appear evenmore unlike the denatured state than that from the protein atphysiological temperatures. Under these circumstances, θ₂₂₂ measurementswill appear to indicate increasing stability of the protein, anerroneous conclusion.

Thus, there is a need in the art for a spectroscopic analysis thatminimizes dependence on the independently varied parameter, such astemperature such that it need not rely on corrections and assumptionsthat cannot be substantiated. Moreover, there is a need for an analysisthat can be used simultaneously with several of the common modes ofspectroscopy presently in use.

SUMMARY OF THE INVENTION

To fulfill the above needs, it is an object of the present invention toprovide a method for determining the respective fractions of a foldedform and an unfolded form of a molecule in solution, in order toestimate a fraction of an unfolded form of a molecule in solution and todetermine apparent free energy of a conversion reaction between a foldedform and an unfolded form of a molecule in solution.

Additional objects and advantages of the invention will be set forth inpart in the description which follows, and in part will be obvious fromthe description, or may be learned by practice of the invention. Theobjects and advantages of the invention will be realized and attained bymeans of the elements and combinations particularly pointed out in theappended claims.

Accordingly, to achieve the above object, the present invention, asembodied and broadly defined herein, provides a method of determiningthe respective fractions of a folded form and an unfolded form of amolecule in solution using differential spectral topographic analysis(DISTA), comprising summing absolute differences in topography betweeneach of two reference spectra and a sample spectrum taken at differentmagnitudes of at least one perturbation parameter, plotting curves ofthe sums versus the at least one perturbation parameter, andquantitatively estimating the degree to which the molecules appearsimilar to folded or unfolded forms of the molecules.

According to another object of the invention, the present invention asembodied and broadly defined herein, provides a method of determiningthe respective fractions of a folded form A and unfolded form B of amolecule in solution, comprising the steps of:

(a) recording reference spectra for the molecule in solution over a setof range(s) one for each of one or more perturbation parameters suchthat for each range the molecule is essentially entirely in form A.

(b) normalizing reference spectra to a topographical space such that thevalues of the normalized spectra are substantially dependent on themolecular configuration of the molecule of interest;

(c) characterizing, for each wavelength in the reference spectra, anyremaining dependence of the normalized reference spectral values on theperturbation parameter(s) by fitting the reference spectral normalizedintensity values to the following equation:

I _(λ) _(i) ^(normalized)(P ₁ ,P ₂ , . . . P _(n))=(A ₁ +A ₂ *P ₁ +A ₃*P ₁ ² + . . . +A _(m) *P ₁ ^(m))*(B₁ +B ₂ *P ₂ +B ₃ *P ₂ ² + . . . +B_(k) *P ₂ ^(k))* . . .

wherein the P_(i) are the values of the ith perturbation parameter, theA_(i), B_(i), etc. are fitting constants, and m, k, etc. are thesmallest exponents such that the fit is within the accuracy of the noiseof measurement, and I is the normalized intensity at the ith wavelength;

(d) extrapolating the values of I throughout the full range of P_(i) atwhich experimental spectra will be recorded;

(e) recording test spectra periodically in response to variation in atleast one perturbation parameter selected from a group includingtemperature, pressure, pH, presence of a stabilizer, presence of aligand, electromagnetic radiation, magnetic field, gravitational field,and presence of a denaturant;

(f) normalizing each spectrum to the appropriate topographical space;

(g) calculating a DISTA value for each test spectrum using the equation:$\left\lbrack {\sum\limits_{\lambda \quad i}{{S_{\lambda \quad {ir}} - S_{\lambda \quad {it}}}}^{n}} \right\rbrack^{1/n},$

 wherein n is a transform scaling exponent, S_(λir) is the normalizedreference signal at wavelength λ_(i) taken from a spectrum extrapolatedin step (d), S_(λit) is the normalized test signal at λ_(i) and the sumis over all λ_(i); and

(h) repeating, optionally, steps (a) through (g) using a set of rangesover which the unfolded form B is essentially the only form to generatea second set of extrapolated reference spectra.

According to another object of the invention, the present invention asembodied and broadly defined herein, provides a method of determiningthe fraction of secondary structure lost in a molecule of interest insolution, comprising recording Far-UV CD reference spectra for a foldedform and an unfolded form of the molecule, recording Far-UV CD testspectra as at least one perturbing parameter is systematically varied,normalizing each spectra by converting to ellipticity, calculating DISTAvalues for the test spectra, and calculating the fraction of secondarystructure lost, F_(u), using the equation:${F_{u} = \frac{D_{s} - D_{r2}}{D_{r1} - D_{r2}}},$

where D_(s) is the sample DISTA signal, D_(r1) is the reference signalof greater magnitude, and D_(r2) is the reference signal of lessermagnitude.

According to another object of the invention, the present invention asembodied and broadly defined herein, provides a method of measuring achange from a first configuration to a second configuration in aphysical configuration of a system of interest, comprising calculatingDISTA values for test spectra by summing absolute differences intopographic values between each of two reference spectra representingthe first and second configurations of the system of interest and asample spectrum taken at different magnitudes of at least oneperturbation parameter, plotting each sum versus the at least oneperturbation parameter to create a DISTA curve, and proportionallyscaling the DISTA values at a value of interest of the perturbationparameter between known reference values for the first and secondconfigurations of the physical configuration of the system of interestto obtain an estimate of the fraction of conversion to the secondconfiguration of the physical configuration of the system of interest.

BRIEF DESCRIPTION OF FIGURES

The file of this patent contains at least one drawing executed in color.Copies of this patent with color drawing(s) will be provided by thePatent and Trademark Office upon request and payment of the necessaryfee.

FIGS. 1A-1I depict the DISTA values plotted against the perturbingparameter from fluorescence spectra for a series of proteins over atemperature range.

FIGS. 2A-2I depict the DISTA from fluorescence spectra for anotherseries of proteins varied over a temperature range.

FIG. 3 depicts the DISTA analysis of cold annealed myoglobin in Far-UVCD.

FIGS. 4A and 4B depict the DISTA analysis of cold annealed myoglobin inFar-UV CD.

FIG. 5 is a flow chart depicting the calculation of DISTA values.

FIG. 6 is a flow chart depicting the calculation of apparent free energyand fraction of structural change.

FIG. 7 shows the response of β-lactoglobulin to temperature at differenturea concentrations and establishes the range over which the protein islikely to be completely folded and shows residual temperature dependenceof the normalized spectral shape.

FIG. 8 shows a comparison of DISTA analysis where the DISTA signal has adependence on the perturbing parameter.

DETAILED DESCRIPTION OF THE INVENTION

According to the present invention, and as embodied herein, an analysisto estimate the fraction of folded and unfolded forms of a molecule insolution is provided, wherein the molecule represents an organic ornon-organic organized system, including proteins, polymers, biopolymers,and peptides. This method of analysis is based on Differential SpectralTopographic Analysis (DISTA). The DISTA method uses data from thespectral methods known in the art and is based upon the normalization ofthe spectra to a fixed topographic space, creating a set of spectralforms, and the summation of the absolute differences in topographybetween one or more such reference spectra and the test spectra taken atdifferent magnitudes of the perturbing parameter. This method allows foran estimate of the fraction of folded and unfolded forms of proteinseven if the dependence of the unnormalized signal on the perturbationparameter varies in a complex and mathematically unknown way. As long asthis topographic absolute difference signal is essentially zero over therange in which only the pure reference form (whether folded or unfolded)would be expected to exist, then the method can reasonably be used as aquantitative measure of unfolding.

In the practice of the invention, standard spectroscopic methods wellknown to those of ordinary skill in the art and based on the UV or VISabsorbance spectrum, fluorescence spectrum, and/or Far and Near UV CDspectrum are used. This method is applicable to all spectral methods,and the normalization techniques used for each spectra will varyaccordingly, as should be obvious to one of skill in the art. Thesemethods can be used so long as it can reasonably be expected that over adefinable range of the perturbing parameter the spectral form isindependent of the perturbing parameter. Any perturbation parameterwhich would not change the topographic signal but would affect theconfiguration of molecule in an area of interest and would reflect thischange in the topographic signal may be used, for example, theperturbing parameter may be temperature, pressure, pH, presence of astabilizer, presence of a ligand, electromagnetic radiation, magneticfield, gravitational field, or presence of a denaturant. For example,the spectral form can reasonably be expected to be independent of theperturbing parameter of temperature through a range of 20° C. to 50° C.Thus, for many proteins the forms of the UV or VIS absorbance spectrum,fluorescence spectrum, and Far and Near-UV CD spectrum are dependent onmolecular configuration and relatively insensitive to temperature overcertain temperature ranges. This is illustrated over temperature rangesof widths ≧20° C. for a number of proteins in FIGS. 1 through 4, and canbe used at any temperature as long as it is possible to opticallymeasure.

The DISTA method of the invention provides a quantitative measure of thefolding nature of the molecule of interest (when using fluorescence orabsorbance spectra) or fraction of loss of secondary structure (whenusing Far-UV CD spectra) by the following steps:

(1) Recording two reference spectra, one of the appropriate pure form A(e.g., the folded or native form) of a molecule, the other of thecomplementary pure form B (e.g., the unfolded form of the molecule).

(2) Normalizing both spectra to the topographic space (0,1) influorescence or absorption spectra. This is accomplished for eachspectrum separately by dividing all values in each spectrum by theabsolute value of the maximum magnitude value (fluorescence orabsorbance spectra), or by integrating the partial area of the curvefrom the starting value to each of the intermediate values andsubsequently dividing by the entire area under the spectral curve. Thislatter method more accurately represents the statistical distribution ofexcited state energies and is thus more rigorous. In practice there israrely any significant difference in the predictions of these twoalternatives and the first is calculationally faster. If the spectrabeing analyzed are CD spectra, then they are normalized by converting toellipticity, a standard procedure for those skilled in the art.

(3) Test spectra are then recorded periodically as one or moreperturbing parameters, such as temperature, pressure, pH, presence of astabilizer, presence of a ligand, electromagnetic radiation, magneticfield, gravitational field, or presence of a denaturant aresystematically varied. The variation of these perturbing parameters iswell within the skill of those in the art.

(4) Each spectrum is subsequently normalized by dividing all of itsvalues by the absolute value of that spectrum's maximum magnitude value(when fluorescence or absorbance is used), or by converting toellipticity (when CD is used).

(5) The DISTA value for the test spectrum is then calculated as:$\left\lbrack {\sum\limits_{\lambda \quad i}{{S_{\lambda \quad {ir}} - S_{\lambda \quad {it}}}}^{n}} \right\rbrack^{1/n}$

 where n is a transform scaling exponent generally equal to one (1),S_(λir) is the normalized reference signal at wavelength λ_(i) (thewavelength of measurement which is varied systematically from a minimumto a maximum), S_(λit) is the normalized test signal at λ_(i) and thesum is over all λ_(i). The difference between the test spectra and thereference spectra may also be calculated using exponential values of thesignals different from one, i.e., n≠1, depending upon the physicalsystem being tested. For protein unfolding, the sum of the absolutedifference is the preferred method.

(6) The DISTA values (for fluorimetric, absorbance, and CD) are thenscaled linearly between the values for the two pure forms, folded andunfolded, and the estimate of the fraction unfolded, F_(u), isdetermined by the equation:$F_{u} = \frac{D_{s} - D_{r2}}{D_{r1} - D_{r2}}$

 where D_(s) is the sample DISTA signal, D_(r1) is the reference signalgreater in magnitude, and D_(r2) is the reference signal lesser inmagnitude.

(7) The estimate of the fraction unfolded, F_(u), can then be directlyconverted to an estimate of free energy of unfolding using: ΔG=−RTLog(K), where ΔG is the free energy of the reaction folded to unfolded,R is the gas constant, T is the absolute temperature, and K is the massaction constant of the reaction:${K = \frac{\lbrack B\rbrack}{\lbrack A\rbrack}},$

 where the [A] is the concentration of folded form of the molecule ofinterest and [B] is the concentration of unfolded form of the moleculeof interest. If the spectrum analyzed is Far-UV CD, then F_(u)represents fraction of secondary structure lost. This may notnecessarily reflect the extent of tertiary unfolding, but is of primaryconcern in establishing whether the refolded species are really nativestate and in establishing the fraction of secondary structure lost, ifany. Quantification of the continuous loss of secondary structure withtime and as a function of protein concentration is shown in FIGS. 3, 4A,and 4B.

As embodied in FIGS. 1 and 2, an analysis has been performed on variousproteins in aqueous solutions over a wide temperature range. The sum ofabsolute differences at each wavelength between a sample spectrum andeach of two reference spectra (fully native or folded, and fullydenatured or unfolded, respectively) were calculated and used to drawtwo curves of Σ (differences with each reference spectrum) vs.temperature. These allow quantitative estimation of the degree to whichthe protein appears similar in structure to a native or denatured form.If the sums fall between the values of the reference spectra, they canbe scaled to yield an estimate of fraction unfolded.

For FIGS. 1A-1I and 2A-2I, each sample was prepared and then the samplewas split in half on the bench. The first half of the sample was runimmediately, and the second half of the sample was run after the firsthalf was complete. The following example completely describes thedevelopment of a representative set of DISTA statistics as done in FIGS.1A-1I and 2A-2I, and their use to calculate a fraction of proteinunfolded and the free energy of unfolding. The example below describesgeneral preparation of the samples using lysozyme at pH 4.8 asillustrated in FIG. 1A. Calculation of DISTA values in curves 3-6(black, green, dark blue, and light blue curves, respectively) at 0° C.will be illustrated.

The methods of Examples 1 and 2 are most preferable when one isinvestigating the influence of perturbing parameters such as pH orchemical denaturants such as urea. However, in certain circumstances themethods of Example 1 and Example 2 may not be the preferred method. Themethod of Example 3 should then be used. These circumstances generallyoccur when one is interested in investigating the influence ofperturbing parameters such as temperature or pressure.

In other words, the method of Example 3 should be used when the spectralshape of the protein is independent from the perturbing parameter withinthe range to be tested (i.e., the protein is either in a folded orunfolded state for the entire range) and the spectral shape is notconstant over that range. These circumstances often occur when theperturbing parameter is temperature or pressure. However, whenconditions such as pH are varied there is a narrower range where theprotein is in a folded state and the single spectral analysis ofExamples 1 and 2 are the preferred method.

EXAMPLE 1

First, the sample was dissolved in 10 millimolar acetate buffer, pH 4.8,at room temperature at concentration 0.23 mg/ml. The protein was allowedto equilibrate in this state for at least 24 hours. The solution wasthen divided into two equal portions. The first portion was inserted inthe fluorimeter, and cooled at 0.3° C./min to a temperature of −10° C.The computer controlled cooling bath was then instructed to beginheating the sample to a temperature in excess of 100° C. at the same lowrate of temperature change. Throughout this procedure, as thetemperature gradually increased, fluorescence emission spectra (320nm-365 nm with excitation at 280 nm) were being recorded at a rate oftwo or three per minute. After recooling of the sample chamber to roomtemperature the second portion of the sample held at room temperaturewas then inserted into the fluorimeter and was immediately warmed at0.3° C./min to a temperature above 100° C. while fluorescence emissionspectra were being recorded at a rate of two or three per minute.

After all spectra were recorded, a high temperature fluorescenceemission spectrum of a sample maintained at room temperature before thistest was chosen as a reference such that it could reasonably be assumedthat the protein is essentially entirely in a heat denatured (unfolded)form at the chosen temperature. In this instance, the spectrum at 95° C.was chosen. The maximum of emission was found to be close to 350 nm.Then the values of emission at all wavelengths in this spectrum, rangingfrom 320 nm to 365 nm were divided by this aforementioned maximum. Thevalues so obtained range in magnitude from 0 to 1 and they are thenormalized spectrum at 95° C. The same process was repeated utilizingthe spectrum at 35° C. of a sample maintained at room temperature beforethis test, this value having been chosen because the evidence from avariety of techniques indicates that 35° C. is a temperature at whichthe protein, in physiological solution, would reasonably be expected tobe essentially entirely in the native (folded) form. In this case,however, the maximum of emission to be used as the divisor was close to335 nm. To develop the four DISTA data points for 0° C., the next stepwas to repeat the normalization process for the spectrum taken at 0° C.during the initial cooling of the protein solution (lower black curve3). In this case, the maximum of emission was found to be at awavelength between approximately 335 nm and 340 nm. After this spectrumwas normalized by dividing all of its values by its maximum emissionvalue, the sum of absolute differences was calculated with respect tothe normalized reference spectrum recorded at 35° C. To do this, thenormalized value of the native reference at each wavelength wassubtracted from the normalized value of the 0° C. spectrum at eachmatching wavelength, e.g., the reference value at 320 nm minus 0° C.value at 320 nm, the reference value at 325 nm minus 0° C. value at 325nm, etc. The absolute value of each of these differences is equal to thepositive value of each difference. The sum of these absolute values overall of the wavelengths at which measurements were taken constituted theDISTA value for the 0° C. spectrum during cooling (curve 3, black if incolor). The other three values at 0° C. as shown in FIG. 1A for lysozymepH 4.8 were calculated in the same fashion except for the following:

a) the reference spectrum used to calculate the 0° C. data point in theupper curve 6 (light blue if in color) was the normalized 95° C.reference spectrum instead of the 35° C. normalized reference spectrum;

b) the 0° C. data point in curve 5 (dark blue if in color) used thenormalized spectrum from the sample recorded during rewarming instead ofrecooling, and the normalized 95° C. reference spectrum instead of the35° C. normalized reference spectrum was used; and

c) the 0° C. data point in curve 4 (light green if in color) used thenormalized spectrum from the sample recorded during rewarming instead ofcooling.

Once the entire set of DISTA values over the temperature range ofinterest was calculated the fraction unfolded and free energy ofunfolding could be calculated for any temperature of interest. Thecalculation for 0° C. is as follows. The maximum DISTA value for thecurves referencing the high temperature state is 0.8 units near 40° C.At 0° C., the value is 0.6 units, so there is a loss of value of 25% ofthe full change in value going from native state (folded form) to hightemperature denatured state (unfolded form). Thus, the estimate is thatthe protein has a ratio of B (unfolded) to A (folded) of [0.25]/[0.75].From this fraction, the apparent free energy of the reaction A⇄B isgenerally derivable from the equation:

ΔG=−RT Log(K).

In the FIGS. 1A-2I, curves 1 and 2 (or the red and magenta curves,respectively, if in color, red representing a warming only curvereferenced to the denatured state and magenta representing a warmingonly curve referenced to the native state) represent the results thefirst half of the sample, and curves 3, 4, 5, and 6 (or the black,green, dark blue, and light blue curves if in color, black representinginitial cooling referenced the native state, green representingrewarming referenced to the native state, dark blue representingrewarming referenced to the denatured state, and light blue representingcooling referenced to the denatured state) represent the test results ofthe other half of the sample. In each of the FIGS. 1A-2I, the curvenumber and color correspond to the same portion of the curve. Therefore,curves 1 (red if in color) represent a warming only curve, curves 2(magenta if in color) represent a warming curve, curves 3 (black if incolor) represent initial cooling, curves 4 (green if in color) representrewarming, curves 5 (dark blue if in color) represent rewarming, andcurves 6 (light blue if in color) represent cooling. Points 7 and 8represent the chosen reference points at which by definition thereference spectra and test spectra are the same. In each of the figures,it can be noted that curve 4 (green) closely follows curves 2 and 3(magenta and black), and curve 5 (dark blue) closely follows curves 6and 1 (light blue and red). The difference between the curve 4 (green)and curves 2 and 3 (magenta and black), and curve 5 (dark blue) andcurves 6 and 1 (light blue and red) represents hysterisis, showing thatthere have been permanent changes in the molecule from the coolingprocess and subsequent reheating.

If a measurable fraction, i.e., a fraction sufficient to change thescope of the test, of molecules converts from form A to form B or viceversa, the two complementary DISTA curves will depart from the baselineas mirror images, i.e., if one were to reverse curves 2, 3, and 4(magenta, black, and green), or look at them in a mirror and comparethem with curves 1, 5, and 6 (red, dark blue, and light blue), it wouldbe seen that the curves match up, that is, they are essentially mirrorimages of one another. If the curves depart from baseline largelyasymmetrically as in the proteins shown in FIGS. 1E, 1F, 1G, 1I, 2D, and2G, that is an indication that the conversion is to a form distinct fromboth A and B. However, if largely symmetric as in the proteins shown inFIGS. 1A, 1B, 1C, 1D, 2A, 2B, 2C, 2E, 2H, and 2I, the DISTA signals canbe construed as representing fractions of each of the two forms (byproportionally scaling them between the values for the pure forms) andthe apparent free energy of the reaction A⇄B is then generally derivablefrom:

ΔG=−RT Log(K)

where ΔG is the free energy of the reaction folded to unfolded, R is thegas constant, T is the absolute temperature, and K is the mass actionconstant of the reaction:$K = {\frac{\lbrack B\rbrack}{\lbrack A\rbrack}.}$

As discussed earlier, the method for determining the extent of exposureof fluorophores to the environment external to the protein known asfluorescence quenching cannot easily be related to the percent ofprotein unfolded because it provides less information about the spectralcharacteristics of the unquenched fluorophores. In the DISTA method, thecontributions of essentially all of the fluorophores are taken intoaccount, so unfolding of a domain at low temperature different from thedomain that unfolds at high temperature would produce an increase in thedifference signal at low temperature relative to both the native stateand high temperature denatured forms (curve asymmetry). This isillustrated in several of the figures, such as in Lactoferrin in FIG. 1Fand in Ovalbumin in FIG. 2G. The Stern-Volmer analysis can be used,however, to confirm that, even in some cases where the low temperatureDISTA curves are substantially asymmetric, it is unfolding that isoccurring by showing that the fraction of quenchable fluorophoresincreases.

Because helices are often quite stable at low temperature (J. M. Scholtzet al.), low temperature tertiary unfolding may leave helical secondarystructures intact and the helices may appear longer, i.e., have CDsignals of larger magnitude, such that the secondary structure mayappear even more unlike the heat denatured state than it does from theprotein at physiological temperatures. Under these circumstances, θ₂₂₂measurements will appear to indicate increasing stability of theprotein. Concurrently DISTA performed on data sets from Far-UV CD willyield substantially asymmetric curves which will be evidence that thelow temperature secondary structures are different from the tworeference states, but if the amount of secondary structure decreases asa result of a second perturbation such as protracted exposure of theprotein to low temperature, then DISTA will measure the extent ofsecondary structure loss even if the structures are not helices and thecurves are asymmetric. FIGS. 3, 4A, and 4B represent examples where theDISTA analysis has used Far-UV CD spectra rather than fluorescencespectra. FIGS. 3, 4A and 4B show in Far-UV CD DISTA for helical datafrom myoglobin annealed at 0° C. for extended periods. Curve 12 in FIG.3 represents myoglobin annealed at 0° C. for 45 days in a concentrationof 0.1 mg/ml, curve 14 represents myoglobin annealed at 0° C. for 45days in a concentration of 0.2 mg/ml, curve 16 represents myoglobinannealed at 0° C. for 45 days in a concentration of 0.3 mg/ml, and curve18 represents myoglobin annealed at 0° C. for 45 days in a concentrationof 0.6 mg/ml. Curve 20 in FIGS. 4A and 4B represents myoglobin annealedat 0° C. for 15 days in concentration of 0.23 mg/ml, curve 22 representsmyoglobin annealed at 0° C. for 14 days at 2.3 mg/ml then diluted 1:10to a concentration of 0.23 mg/ml just before measurement, and curve 24represents a relaxed myoglobin sample 3 days at room temperature inconcentration of 0.23 mg/ml.

As an example, a complete description of the development of arepresentative set of DISTA statistics based on Far-UV CD and their useto calculate the fraction of secondary structure lost follows using thedata in FIGS. 4A and 4B for myoglobin pH 4.8. We will illustrate thecalculation of the DISTA values at 30° C.

EXAMPLE 2

First, the sample was dissolved at room temperature in 10 millimolaracetate buffer to a concentration of 2.3 mg/ml. The protein was allowedto equilibrate in this state for 72 hours. The solution was then dividedinto three equal portions.

The first portion (red curve 24) was diluted to 0.23 mg/ml and insertedin the CD at room temperature and immediately warmed at 0.3° C./min to atemperature above 100° C. while spectra were being recorded at a rate oftwo to three per minute.

The second portion (blue curve 20) was diluted to 0.23 mg/ml, thenplaced on ice and held for 15 days at 0° C. It was then placed in the CDat 0° C. The cooling bath was then instructed to begin heating thesample to a temperature in excess of 100° C. at the same low rate of0.3° C./min as for portion one. Throughout this procedure Far-UV CDspectra were being recorded at a rate of two to three per minute. Afterthe sample was heated to the maximum temperature, it was rapidlyrecooled and removed from the CD.

The third portion (green curve 22) was undiluted at 2.3 mg/ml alsoplaced on ice and held for 14 days at 0° C. After that it was diluted to0.23 mg/ml and immediately placed in the CD at 0° C. The cooling bathwas then instructed to begin heating the sample to a temperature of 68°C. at the same low rate of 0.3° C./min as for the first portion.Throughout this procedure Far-UV CD spectra were being recorded at arate of two to three per minute. After the sample was heated to themaximum temperature it was recooled at the same rate as warming whileadditional spectra were recorded.

After all spectra were recorded, they were normalized by converting toellipticity using the standard equation:

θ=0.0001*(m°)*(MW)/(C*r*L)

where θ is in units of 10⁻³ deg cm² decimol⁻¹, m° is the actual CDinstrument result in millidegrees, MW is the molecular weight of theprotein in daltons, C is protein concentration in mg/ml, r is the numberof amino acid residues per molecule, and L is the path length in cm.

A high temperature CD spectrum was chosen as a reference such that itcould reasonably be assumed that the protein is essentially entirely ina heat denatured (unfolded) form at the chosen temperature. In thiscase, the spectrum of the material relaxed at room temperature and thenheated to 90° C. was chosen. For the native state reference the sameprocess was repeated utilizing the spectrum of material maintained at30° C. prior to the test. This was chosen because evidence from avariety of techniques indicates that 30° C. is a temperature at whichthe protein, in physiological solution, would be expected to beessentially entirely in the native (folded) form.

To develop the estimate of percent loss of secondary structure in thecold annealed samples (the second and third portions), a computerprogram has been developed to calculate DISTA values as follows. The sumof absolute difference with respect to the normalized native referencespectrum recorded at 30° C. are calculated. To do this, the normalizedvalue of the native reference at each wavelength was subtracted from thenormalized value of the 30° C. spectrum at each matching wavelength, e.g., the reference value at 240 nm minus the 30° C. value at 240 nm, thereference value at 239 nm minus the 30° C. value at 239 nm, etc. Theabsolute value of each of these differences is equal to the positivevalue of each difference. The sum of these absolute values over all ofthe wavelengths at which measurements were taken constituted the DISTAvalue for the 30° C. spectrum in each sample.

Once the entire set of values over the temperature range of interest wascalculated the fraction of secondary structure lost could be calculatedfor any temperature of interest. The calculation for the fraction ofsecondary structure lost for 30° C. was performed as follows. The DISTAvalue for the reference curve at 90° C. is 2600 units. At 30° C. thevalue is 0 units. For the sample portion annealed 15 days at 0.23 mg/mlthe value at 30° C. is 350 units or 13% of the full change in valuegoing from native to high temperature denatured state (from 30° C. to90° C.). Thus, the estimate is that for the protein annealed at 0° C. atthis concentration, about 13% of the secondary structure which is labileto heat denaturation has been lost.

FIG. 5 describes the flow chart for a computer program calculating theimportant parameters in the DISTA method of spectral analysis. In thefirst step 100, the specific molecular and physical parameters are inputto the system by the investigator. This would include such data as themolecular weight of a protein, the concentration of the protein in thesolution, the name of the file wherein unprocessed spectral data isstored, and other parameters that will be necessary in the calculationof the DISTA statistics. In the next step 110, the program inputs theunnormalized spectral data as it has been produced by the analyzingmachine. It may be a circular dichroic measuring device, an absorptionspectrophotometer, spectrofluorimeter or other similar device. In thenext step 120 which is optional, the data may be smoothed by variousclassical smoothing algorithms to eliminate noise components. Inaddition, if there are baselines that indicate systematic noiseparameters such as scattering in a spectrofluorimeter they can besubtracted at this step from the unnormalized spectral data. In the nextstep 130, the data is normalized. The algorithm for normalizing the datawill depend on the appropriate methodology for each spectral measuringtype. As an example, in fluorimetry the total area under the spectralcurve will be calculated, then the partial areas from the startingwavelength to each in turn of each of the intermediate wavelengths willbe calculated, and the partial areas so calculated will be then bedivided by the total area to get a series of partial normalized areas.Alternatively, also in fluorimetry, the emission intensities of eachwavelength will be analyzed, the maximum intensity will be determined.The maximum intensity is then divided into each of the intensities ineach spectrum to produce a normalized intensity spectrum. In the nextstep 140, the DISTA values for each spectrum will be calculated. Twospectra have been chosen to represent the values for the test moleculeswholly in form A or wholly in form B, and the subtraction will be of allof the other normalized spectral values in turn for each normalizedspectrum from each of the normalized reference spectra individually.Thus, if one of the reference spectra was recorded at 35° C. withtemperature as the perturbing parameter, then the DISTA value for the60° C. spectrum will be calculated by this program by taking each of thenormalized values at 60° C. for each wavelength recorded at 60° C.subtracted from the value at the same wavelength in the normalized 35°C. spectrum. The program will then calculate the positive value of thesubtraction and sum all of those positive values to give the DISTA valuefor the 60° C. spectrum versus the 35° C. spectrum. This is the DISTAvalue calculated by the program. In the final step 150, the programoutputs the data to disk or stores it in an array in memory for use tocalculate the fraction unfolded where that is appropriate.

FIG. 6 shows a flow chart for the calculation of fraction unfolded,where the DISTA value at any given value of the perturbing parameter isscaled between the two limiting values. In the first step 200, the DISTAvalue vs. perturbing parameter is input. In the second step 210, DISTAvalues are scaled between values for pure forms of the molecule ofinterest. As an example, if the value at 35° C. is a reference for aparticular protein, and temperature is the perturbing parameter, thenthe DISTA value at 35° C. of the 35° C. reference spectrum is 0, and thevalue at 90° C. (where the protein is heat denatured) might be 1.5units. If at 60° C. it is 0.75 units, i.e., the value is scaled half waybetween the 35° C. value and the 90° C. value, that would then indicatethat the fraction of the high temperature form present at 60° C. is 0.5and that would be the fraction unfolded parameter calculated from theDISTA data (step 220). In those cases where fraction unfolded can becalculated, step 230 is performed and the free energy can then becalculated directly in the same program by multiplying the logarithm of(the ratio of fraction unfolded to fraction folded) times the absolutetemperature in kelvin times the gas constant R, which equals thenegative of the Gibbs free energy of conversion of the folded form tothe unfolded form. In cases where the test measurement would not beexpected to give an accurate estimate of the fraction unfolded, such assome cases of secondary structure breaking measured by Far-UV CD, theDISTA analysis can still be used as a valuable tool. For example, thepercentage of secondary structure conversion at certain levels ofperturbation parameters (e.g. temperature) can be estimated by scalingthe DISTA value as described above (step 220) within the two referencestates at two different levels of the perturbing parameters (step 240).

EXAMPLE 3

The method of Example 3 is directed to solving the problem of correctingfor intrinsic variation of the topographic spectral forms with theperturbation parameter. It shows the normalized spectra varying as afunction of the perturbing parameter over a range of such a parameterwherein the molecular form remains essentially unchanged, corrects forthis dependence on the perturbing parameter, and calculates the fractionof the protein in the folded and unfolded state. The preparation of thesample of Example 3 was carried out generally as in Example 2.

For instance, FIG. 7 shows the response of β-lactoglobulin to highconcentrations of urea. In the range 25° C. to 45° C. the protein has aconstant slope and a minimal destabilization up to several molar urea.Thus, in the absence of the denaturant in this stable range the proteinis essentially completely in the folded form, but still manifests atemperature dependence of spectral shape as shown by the ratio data.This dependence can be calculated over the entire range of interest byfitting the values of normalized intensity at each wavelength separatelyover the stable range for the protein in question, then extrapolatingover the entire range according to the following polynomialextrapolation equation for a single parameter (P):

I _(λ) _(i) ^(normalized)(P)=A+B*P+C*P ²+  (1)

where the I_(λi) is the normalized spectral value at a perturbationparameter value of P. The order of the polynomial extrapolation equationis the smallest such that the fit is within the accuracy of the noise ofmeasurement. The procedure from this stage on is the same as that of thesingle spectrum method except instead of calculating the absolute valueof the difference between each value of each normalized sample spectrumand a reference spectrum recorded at some perturbation parameter valueP₀, the absolute value of the difference between each value of eachnormalized sample spectrum and each value of one spectrum of a set ofextrapolated reference spectra which corresponds to a best estimate ofthe spectrum at the sample spectrum temperature, P, is taken. This isdescribed in a step by step manner as follows:

(1) Recording a series of reference spectra, over a range of perturbingparameter P such that the molecules are essentially entirely in one ofthe appropriate pure forms e.g., the folded or native form of amolecule. If possible this should be repeated over an independent rangeof P such that essentially all the molecules are in the other of thepure forms e.g., the unfolded form of the molecule.

(2) Normalizing the reference spectra to the topographic space (0,1) influorescence or absorption spectra. This is accomplished for eachspectrum separately by dividing all values in each spectrum by theabsolute value of the maximum magnitude value (fluorescence orabsorbance spectra), or by integrating the partial area of the curvefrom the starting value to each of the intermediate values andsubsequently dividing by the entire area under the spectral curve. Thislatter method more accurately represents the statistical distribution ofexcited state energies and is thus more rigorous. In practice there israrely any significant difference in the predictions of these twoalternatives and the first is calculationally faster. If the spectrabeing analyzed are CD spectra, then they are normalized by converting toellipticity, a standard procedure for those skilled in the art.

(3) Test spectra are then recorded periodically as one or moreperturbing parameters, such as temperature, pressure, pH, presence of astabilizer, presence of a ligand, electromagnetic radiation, magneticfield, gravitational field, or presence of a denaturant aresystematically varied. The variation of these perturbing parameters iswell within the skill of those in the art.

(4) Each test spectrum is subsequently normalized by dividing all of itsvalues by the absolute value of that spectrum's maximum magnitude value(when fluorescence or absorbance is used), dividing partial areas by thetotal area, or by converting to ellipticity (when CD is used).

(5) Reference spectra are then calculated for each of the values of theperturbing parameters at which test spectra were recorded. Thenormalized intensity value at each wavelength of each of these testspectra is calculated by fitting the reference spectra data to thefollowing polynomial extrapolation equation for multiple independentparameters:

I _(λ) _(i) ^(normalized)(P ₁ ,P ₂ , . . . P _(n))=(A ₁ +A ₂ *P ₁ +A ₃*P ₁ ² + . . . +A _(m) *P ₁ ^(m))*(B ₁ +B ₂ *P ₂ +B ₃ *P ₂ ² + . . . +B_(k) *P ₂ ^(k))* . . .   (2)

wherein the Pi are the values of the ith perturbation parameter, theA_(i), B_(i), etc. are fitting constants, and m, k, etc. are thesmallest exponents such that the fit is within the accuracy of the noiseof measurement, and I is the normalized intensity at the ith wavelength.In general, only one independent perturbation parameter at a time isvaried, in which case the polynomial extrapolation equation for multipleindependent parameters P_(n) on equation 2 is equivalent to thepolynomial extrapolation equation for a single parameter P on equation1.

(6) The DISTA value for the test spectrum is then calculated as:$\left\lbrack {\sum\limits_{\lambda \quad i}{{S_{\lambda \quad {ir}} - S_{\lambda \quad {it}}}}^{n}} \right\rbrack^{1/n}$

 where n is a transform scaling exponent generally equal to one (1),S_(λir) is the normalized reference signal at wavelength λ_(i) (thewavelength of measurement which is varied systematically from a minimumto a maximum) from the calculated reference spectrum for theperturbation parameter value at which the test spectrum was recorded,S_(λit) is the normalized test signal at λ_(i) and the sum is over allλ_(i). The difference between the test spectra and the reference spectramay also be calculated using exponential values of the signals differentfrom one, i.e., n≠1, depending upon the physical system being tested.For protein unfolding, the sum of the absolute difference is thepreferred method.

(7) The DISTA values (for fluorimetric, absorbance, and CD) are thenscaled linearly between the values for the two pure forms, folded andunfolded, and the estimate of the fraction unfolded, F_(u), isdetermined by the equation:$F_{u} = \frac{D_{s} - D_{r2}}{D_{r1} - D_{r2}}$

 where D_(s) is the sample DISTA signal, D_(r1) is the reference signalgreater in magnitude, and D_(r2) is the reference signal lesser inmagnitude.

(8) The estimate of the fraction unfolded, F_(u), can then be directlyconverted to an estimate of free energy of unfolding using: ΔG=−RTLog(K) , where ΔG is the free energy of the reaction folded to unfolded,R is the gas constant, T is the absolute temperature, and K is the massaction constant of the reaction:${K = \frac{\lbrack B\rbrack}{\lbrack A\rbrack}},$

 where the [A] is the concentration of folded form of the molecule ofinterest and [B] is the concentration of unfolded form of the moleculeof interest. If the spectrum analyzed is Far-UV CD, then F_(u)represents fraction of secondary structure lost. This may notnecessarily reflect the extent of tertiary unfolding, but is of primaryconcern in establishing whether the refolded species are really nativestate and in establishing the fraction of secondary structure lost, ifany.

In practice it has so far been found that the normalized intensityvalues of the extrapolated spectra vary in a linear manner withtemperature within the accuracy of the noise of measurement over thetemperature range in which there is substantially only one molecularform. A comparison of the single reference spectrum technique and thisextrapolated technique is shown in FIG. 8 for β-lactoglobulin. It can beseen that only the extrapolated spectral analysis displays a region ofcomplete stability, 25° C. to 55° C. which corresponds to the protein'sresponse to denaturants. Furthermore, the heat denaturation temperatureand enthalpy of heat denaturation are both higher in the extrapolatedanalysis and in much better agreement with calorimetric data. It is alsovery important to note that the estimated fraction unfolded at lowtemperature, i.e. 0° C. and below is ˜25%, in good agreement with CDdata, whereas in the single spectrum native state analysis it is onlyabout 5%.

Although the conversion from one form to another of a given entity ofinterest has been expressed as a determination of protein unfolding,this method is equally applicable to other entities of interest. Givenany physical configuration of a system of interest, such as a molecule,an aggregation of molecules, a liquid crystal structure, or a physicalsurface, a perturbing parameter of interest, where the physicalconfiguration may change structure in ways of interest to theinvestigator, and any kind of signal from a measuring device whichimpinges on a surface of the configuration and whose signal can betransformed such that the signal is only responsive to the entity ofinterest and is substantially independent of the perturbing parameter,DISTA calculations may be used to measure the change from conversion ofthe entity from one configuration to another.

Having now fully described the invention, it will be apparent to one ofordinary skill in the art that many changes and modifications can bemade thereto without departing from the spirit or scope of the inventionas set forth herein. The appended claims are not intended to belimiting.

What is claimed is:
 1. A method of determining the respective fractionsof a folded form and an unfolded form of a molecule in solution,comprising: (a) summing absolute differences in topographic valuesbetween each of two reference spectra representing a folded form and anunfolded form of the molecule of interest and a sample spectrum taken atdifferent magnitudes of at least one perturbation parameter; (b)plotting each sum versus the at least one perturbation parameter tocreate a differential spectral topographic analysis curve; and (c)quantitatively estimating the degree to which the molecule appearssimilar to a folded or unfolded form of the molecule by using datapoints picked off of the curve and scaling these points between knownreference values for folded and unfolded forms of the molecule ofinterest.
 2. The method of claim 1, wherein the at least oneperturbation parameter is selected from a group including temperature,pressure, pH, presence of a stabilizer, presence of a ligand,electromagnetic radiation, magnetic field, gravitational field, andpresence of a denaturant.
 3. The method of claim 1, further comprising:(a) recording two reference spectra for each of a folded form andunfolded form of the molecule; and (b) normalizing the reference spectrato a fixed topographic space.
 4. The method of claim 1, furthercomprising: recording test spectra periodically in response to avariation in the at least one perturbation parameter for comparison toreference spectra of the molecule of interest.
 5. The method of claim 1,wherein the step of summing includes calculating a DISTA value for eachtest spectrum using the equation:$\left\lbrack {\sum\limits_{\lambda \quad i}{{S_{\lambda \quad {ir}} - S_{\lambda \quad {it}}}}^{n}} \right\rbrack^{1/n}$

where n is a transform scaling exponent, S_(λir) is a normalizedreference signal at wavelength λ_(i), S_(λit) is a normalized testsignal at λ_(i), and the sum is over all λ_(i).
 6. The method of claim1, wherein the molecule is an organic or non-organic organized system.7. The method of claim 1, wherein the at least one perturbationparameter is temperature variable over a range of interest.
 8. Themethod of claim 1, wherein substantially asymmetric curves indicate aform of the molecule other than its reference folded or unfolded forms;and wherein substantially symmetric curves indicate respective fractionsof its reference folded and unfolded forms of the molecule.
 9. A methodof estimating a fraction of an unfolded form of a molecule in solution,comprising: (a) calculating DISTA values for test spectra taken atdifferent magnitudes of at least one perturbation parameter; and (b)proportionally scaling the DISTA values between known reference valuesfor a folded form of the molecule and an unfolded form of the moleculeto obtain an estimate of the fraction of the unfolded form of themolecule.
 10. The method of claim 9, wherein the DISTA value iscalculated using the equation:$\left\lbrack {\sum\limits_{\lambda \quad i}{{S_{\lambda \quad {ir}} - S_{\lambda \quad {it}}}}^{n}} \right\rbrack^{1/n}$

where n is a transform scaling exponent, S_(λir) is a normalizedreference signal at wavelength λ_(i), S_(λit) is a normalized testsignal at λ_(i), and the sum is over all λ_(i).
 11. The method of claim10, wherein n=1.
 12. The method of claim 10, wherein n≠1.
 13. The methodof claim 9, wherein the DISTA values are scaled using the formula:$F_{u} = \frac{D_{s} - D_{r2}}{D_{r1} - D_{r2}}$

where D_(s) is the sample DISTA signal, D_(r1) is the reference signalof greater magnitude, D_(r2) is the reference signal of lessermagnitude, and F_(u) is the estimate of the percentage of molecule inthe unfolded form expressed as a fraction.
 14. A method of determiningapparent free energy of a conversion reaction between a folded form andan unfolded form of a molecule in solution, comprising: (a) summingabsolute differences in topographic values between each of two referencespectra representing a folded form and an unfolded form of the moleculeof interest and a sample spectrum taken at different magnitudes of atleast one perturbation parameter to obtain DISTA values; (b)proportionally scaling the DISTA values between known reference valuesfor a folded form of the molecule and an unfolded form of the moleculeto obtain an estimate of the fraction of the unfolded form of themolecule; and (c) converting the estimate of the fraction of theunfolded form of the molecule to an estimate of the free energy ofunfolding.
 15. The method of claim 14, wherein DISTA values arecalculated using the equation:$\sum\limits_{\lambda \quad i}{{S_{\lambda \quad {ir}} - S_{\lambda \quad {it}}}}$

where S_(λir) is a normalized reference signal at wavelength λ_(i),S_(λit) is a normalized test signal at λ_(i), and the sum is over allλ_(i).
 16. The method of claim 14, wherein the DISTA values are scaledusing the formula: $F_{u} = \frac{D_{s} - D_{r2}}{D_{r1} - D_{r2}}$

where D_(s) is the sample DISTA signal, D_(r1) is the reference signalof greater magnitude, D_(r2) is the reference signal of lessermagnitude, and F_(u) is the estimate of the percentage of molecule inthe unfolded form expressed as a fraction.
 17. The method of claim 14,wherein the estimate of the fraction of the unfolded form of themolecule is converted using the equation: ΔG=−RT Log(K) where ΔG is thefree energy of the reaction folded to unfolded, R is the gas constant, Tis the absolute temperature, and K is the mass action constant of thereaction: $K = {\frac{\lbrack B\rbrack}{\lbrack A\rbrack}.}$


18. A method of determining the respective fractions of a folded form Aand unfolded form B of a molecule in solution, comprising the steps of:(a) recording two reference spectra for each of the forms A and B; (b)normalizing both reference spectra to a topographical space such thatthe values of the normalized spectra are substantially dependent on themolecular configuration of the molecule of interest; (c) recording testspectra periodically in response to variation in at least oneperturbation parameter selected from a group including temperature,pressure, pH, presence of a stabilizer, presence of a ligand,electromagnetic radiation, magnetic field, gravitational field, andpresence of a denaturant; (d) normalizing each spectrum to theappropriate topographical space; and (e) calculating a DISTA value foreach test spectrum using the equation:$\left\lbrack {\sum\limits_{\lambda \quad i}{{S_{\lambda \quad {ir}} - S_{\lambda \quad {it}}}}^{n}} \right\rbrack^{1/n}$

where n is a transform scaling exponent, S_(λir) is the normalizedreference signal at wavelength λ_(i), S_(λit) is the normalized testsignal at λ_(i) and the sum is over all λ_(i).
 19. The method of claim18, wherein the at least one perturbation parameter is temperaturevariable over a range of interest.
 20. The method of claim 18, whereinsubstantially asymmetric DISTA curves indicate a form of the moleculeother than folded form A and unfolded form B; and wherein substantiallysymmetric DISTA curves indicate respective fractions of folded form Aand unfolded form B of the molecule.
 21. The method of claim 18, whereinthe normalizing of reference spectra is accomplished by dividing allvalues in each spectrum by the absolute value of the maximum value ineach spectrum, irrespective of sign.
 22. The method of claim 18, furthercomprising: (a) plotting the DISTA values versus the at least oneperturbation parameter; and (b) estimating the respective fractions ofthe folded form A and unfolded form B of the molecule using the DISTAcurves.
 23. A method of determining the fraction of secondary structurelost in a molecule of interest in solution, comprising: (a) recordingFar-UV CD reference spectra for a folded form and an unfolded form ofthe molecule; (b) recording Far-UV CD test spectra as at least oneperturbing parameter is systematically varied; (c) normalizing eachspectra by converting to ellipticity; (d) calculating DISTA values forthe test spectra; and (e) calculating the fraction of secondarystructure lost, Fu, using the equation:$F_{u} = \frac{D_{s} - D_{r2}}{D_{r1} - D_{r2}}$

where D_(s) is the sample DISTA signal, D_(r1) is the reference signalof greater magnitude, and D_(r2) is the reference signal of lessermagnitude.
 24. A method of measuring a change from a first configurationto a second configuration in a physical configuration of a system ofinterest, comprising: (a) calculating a DISTA value for each testspectrum using the equation:$\left\lbrack {\sum\limits_{\lambda \quad i}{{S_{\lambda \quad {ir}} - S_{\lambda \quad {it}}}}^{n}} \right\rbrack^{1/n}$

where n is a transform scaling exponent, S_(λir) is the normalizedreference signal at wavelength λ_(i) at the value r of the perturbingparameter, S_(λit) is the normalized test signal at λ_(i) at the valueof the perturbing parameter and the sum is over all λ_(i); (b) plottingat least one sum for a perturbation value t versus one perturbationparameter at value t to create a DISTA curve; and (c) proportionallyscaling the DISTA values at a value of interest of the perturbationparameter between known reference values for the first and secondconfigurations of the physical configuration of the system of interestto obtain an estimate of the fraction of conversion to the secondconfiguration of the physical configuration of the system of interest.25. The method of claim 24, wherein n=1.
 26. The method of claim 24,wherein n≠1.
 27. A method of determining the respective fractions of afolded form A and unfolded form B of a molecule in solution, comprisingthe steps of: (a) recording reference spectra for the molecule insolution over a set of range(s) one for each of one or more perturbationparameters such that for each range the molecule is essentially entirelyin form A. (b) normalizing reference spectra to a topographical spacesuch that the values of the normalized spectra are substantiallydependent on the molecular configuration of the molecule of interest;(c) characterizing, for each wavelength in the reference spectra, anyremaining dependence of the normalized reference spectral values on theperturbation parameter(s) by fitting the reference spectral normalizedintensity values to the following equation: I _(λ) _(i) ^(normalized)(P₁ ,P ₂ , . . . P _(n))=(A ₁ +A ₂ *P ₁ +A ₃ *P ₁ ² + . . . +A _(m) *P ₁^(m))*(B ₁ +B ₂ *P ₂ B ₃ *P ₂ ² + . . . +B _(k) *P ₂ ^(k))* . . .wherein the P_(i) are the values of the ith perturbation parameter, theA_(i), B_(i), etc. are fitting constants, and m, k, etc. are thesmallest exponents such that the fit is within the accuracy of the noiseof measurement, and I is the normalized intensity at the ith wavelength;(d) extrapolating the values of I throughout the full range of P_(i) atwhich experimental spectra will be recorded; (e) recording test spectraperiodically in response to variation in at least one perturbationparameter selected from a group including temperature, pressure, pH,presence of a stabilizer, presence of a ligand, electromagneticradiation, magnetic field, gravitational field, and presence of adenaturant; (f) normalizing each spectrum to the appropriatetopographical space; (g) calculating a DISTA value for each testspectrum using the equation:$\left\lbrack {\sum\limits_{\lambda \quad i}{{S_{\lambda \quad {ir}} - S_{\lambda \quad {it}}}}^{n}} \right\rbrack^{1/n},$

wherein n is a transform scaling exponent, S_(λir) is the normalizedreference signal at wavelength λ_(i) taken from a spectrum extrapolatedin step (d), S_(λit) is the normalized test signal at λ_(i) and the sumis over all λ_(i); and (h) repeating, optionally, steps (a) through (g)using a set of ranges over which the unfolded form B is essentially theonly form to generate a second set of extrapolated reference spectra.28. The method of claim 27, wherein the at least one perturbationparameter is temperature variable over a range of interest.
 29. Themethod of claim 27, wherein the normalizing of reference spectra isaccomplished by dividing all values in each spectrum by the absolutevalue of the maximum value in each spectrum, irrespective of sign. 30.The method of claim 27, further comprising the additional steps of: (a)plotting the DISTA values versus the values of at least one perturbationparameter; and (b) estimating the respective fractions of the foldedform A and unfolded form B of the molecule using the DISTA curves.
 31. Amethod of determining the fraction of secondary structure lost in amolecule of interest in solution, comprising the steps of: (a) recordingFar-UV CD reference spectra for a folded form and an unfolded form ofthe molecule; (b) recording Far-UV CD test spectra as at least oneperturbing parameter is systematically varied; (c) normalizing eachspectra by converting to ellipticity; (d) determining the respectivefractions of a folded form A and an unfolded form B as in claim 27resulting in a DISTA value; and (e) calculating the fraction ofsecondary structure lost, Fu, using the equation:$F_{u} = \frac{D_{s} - D_{r2}}{D_{r1} - D_{r2}}$

wherein D_(s) is the sample DISTA signal, D_(r1) is the reference signalof greater magnitude, and D_(r2) is the reference signal of lessermagnitude.
 32. A method of measuring a change from a first configurationto a second configuration in a physical configuration of a system ofinterest, comprising the steps of: (a) calculating a DISTA value foreach test spectrum using the equation:$\left\lbrack {\sum\limits_{\lambda \quad i}{{S_{\lambda \quad {ir}} - S_{\lambda \quad {it}}}}^{n}} \right\rbrack^{1/n}$

where n is a transform scaling exponent, S_(λir) is the normalizedreference signal at wavelength λ_(i) at the value r of the perturbingparameter, S_(λit) is the normalized test signal at λ_(i) at the valueof the perturbing parameter and the sum is over all λ_(i); (b) plottingat least one sum for a perturbation value t versus one perturbationparameter at value t to create a DISTA curve; (c) determining therespective fractions of a folded form A and an unfolded form B as inclaim 27 resulting in a DISTA value; and (d) proportionally scaling theDISTA values at a value of interest of the perturbation parameterbetween known reference values for the first and second configurationsof the physical configuration of the system of interest to obtain anestimate of the fraction of conversion to the second configuration ofthe physical configuration of the system of interest.
 33. The method ofclaim 32, wherein n=1.
 34. The method of claim 32, wherein n≠1.